Humble Pi: When Math Goes Wrong in the Real World

by Matt Parker

One of the first bridges to be destroyed by synchronized pedestrians was a suspension bridge just outside Manchester, England (in what is now the city of Salford). I believe that this Broughton Suspension Bridge was the earliest bridge destroyed when people walked over it at the resonant frequency. Unlike the Millennium Bridge, which had a feedback loop to synchronize the pedestrians, on Broughton Bridge the people crossing it had to do all the work themselves. The bridge was built in 1826, and people crossed it with no problem at all until 1831. It took a troop of soldiers all marching perfectly in sync to hit the resonant frequency. The 60th Rifle Corps of seventy-four soldiers were heading back to their barracks at about midday on April 12, 1831. They started to cross in rows of four and pretty quickly noticed that the bridge was bouncing in rhythm with their steps. This was apparently quite a fun experience and they started to whistle a tune to go with the bouncing. Until about sixty soldiers were bouncing on the bridge at once and it collapsed. Around twenty people sustained injuries from the sixteen-foot fall into the river; luckily, nobody died. The discussion during the aftermath identified the vibrations as having put the bridge under a greater load than the same number of people standing still would have. Similar bridges were scrutinized; the knowledge of this type of failure was now out there. Thankfully, it did not take loss of life for humans to learn about th...